The aim of this thesis is to study the security of two particular quantum communication protocols. We want to investigate what is the maximum amount of channel noise for which the protocols can still be secure. We do this by using well known bounds for limiting the information that an eavesdropper can obtain. The first protocol that we study is a direct communication protocol using two-qubit states. We find the security threshold by analyzing the protocol in an enanglement based setting. The Holevo bound was used to put an upper bound on the information of an eavesdropper. To arrive at a manageable optimisation probem, we restrict the eavesdropper's attack strategy such that the noise introduced will be unbiased. Furthermore, we also impose some additional constraints on the eavesdropper that arises from the symmetry of the protocol. After doing this we then optimise the remaining parameters to arrive at the eavesdropper's optimal strategy and find out what is the maximum amount of information she can obtain. Once the eavesdropper's maximum information is known, the security threshold for secure communication was obtained by comparing that information with the information between the legitimate communicating parties. The second protocol studied is a continuous variable quantum key distribution protocol using post-selection. For this protocol, we investigate the maximum amount of information the eavesdropper can get under individual and collective attacks in the presence of Gaussian excess noise in the channel. By providing the eavesdropper with additional information, we can use known results on the accessible information for pure input states to bound the eavesdropper's information. For individual attacks, Levitin's result on the optimal measurement was used while for collective attacks, Holevo's bound was used to arrive at an upper bound for the eavesdropper's information. From this we can then arrive at the post-selection region where the legitimate communicating parties have more information than the eavesdropper. We can then find the maximum amount of noise that the protocol can tolerate before the eavesdropper knows too much and the protocol fails.
The aim of this thesis is to study the security of two particular quantum communication protocols. We want to investigate what is the maximum amount of channel noise for which the protocols can still be secure. We do this by using well known bounds for limiting the information that an eavesdropper can obtain. The first protocol that we study is a direct communication protocol using two-qubit states. We find the security threshold by analyzing the protocol in an enanglement based setting. The Holevo bound was used to put an upper bound on the information of an eavesdropper. To arrive at a manageable optimisation probem, we restrict the eavesdropper's attack strategy such that the noise introduced will be unbiased. Furthermore, we also impose some additional constraints on the eavesdropper that arises from the symmetry of the protocol. After doing this we then optimise the remaining parameters to arrive at the eavesdropper's optimal strategy and find out what is the maximum amount of information she can obtain. Once the eavesdropper's maximum information is known, the security threshold for secure communication was obtained by comparing that information with the information between the legitimate communicating parties. The second protocol studied is a continuous variable quantum key distribution protocol using post-selection. For this protocol, we investigate the maximum amount of information the eavesdropper can get under individual and collective attacks in the presence of Gaussian excess noise in the channel. By providing the eavesdropper with additional information, we can use known results on the accessible information for pure input states to bound the eavesdropper's information. For individual attacks, Levitin's result on the optimal measurement was used while for collective attacks, Holevo's bound was used to arrive at an upper bound for the eavesdropper's information. From this we can then arrive at the post-selection region where the legitimate communicating parties have more information than the eavesdropper. We can then find the maximum amount of noise that the protocol can tolerate before the eavesdropper knows too much and the protocol fails.
An attempt to eavesdrop a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, both in the two-state B92 and the four-state BB84 quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently form other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are included. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi information, and with respect only to bits received error-free by Bob. This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
Quantum information theory is a modern branch of theoretical physics. One of its main goals is to interpret concepts of quantum physics. This leads to a deeper understanding of quantum theory. The most common examples of practical applications of basic quantum theory are quantum computation and quantum cryptography. Quantum cryptography provides secure communication between legitimate users even in the presence of an adversary by making possible the distribution of a secret key. It then allows error correction and privacy amplification, which is elimination of adversary information, through classical communication. In this thesis two important aspects of quantum key distribution are covered, namely robustness bounds with respect to provable entanglement for ideal protocols and practical quantum key distribution using two-way classical communication. In part one of the thesis, ideal quantum key distribution protocols and their robustness in terms of provable entanglement are discussed. The robustness bounds are proved for most general coherent attacks. These bounds for provable entanglement are already known to be 25% for the four-state protocol and 33% for the six-state protocol. We anticipate to provide a region in which the legitimate users share entanglement. This region is large for the four-state protocol and is reduced to a smaller region for the six-state protocol because of additional constraint on it. We also investigate the information cost which the adversary has to pay in order to reach these bounds. In part two we adopt a more practical approach. We investigate the limitation on distance of secure communication because of practical restrictions. In particular we investigate the restrictions due to the lack of single photon sources, the lossy channel and faulty detectors. These practical limitations have already been observed using one-way classical communication between legitimate users. It has been observed that it is actually the dark count rate that limit the distance up to which legitimate users can share a secret key. We have used two-way classical communication to postpone the effect of dark counts and increase the distance to considerable amount. For the purpose we have considered an optimal attack with respect to the disturbance that an eavesdropper creates while attacking. Any other format of attacking will increase the disturbance. We show that using two-way classical communication for post processing we can increase the distance of secure communication considerably.
An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175--179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
The advent of quantum key distribution (QKD) has revolutionized secure communication by providing unconditional security, unlike classical cryptographic methods. However, its effectiveness relies on robust identity authentication, as vulnerabilities in the authentication process can cause a compromise with the security of the entire communication system. Over the past three decades, numerous quantum identity authentication (QIA) protocols have been proposed. This thesis first presents a chronological review of these protocols, categorizing them based on quantum resources and computational tasks involved while analyzing their strengths and limitations. Subsequently, by recognizing inherent symmetries present in the existing protocols, we design novel QIA schemes based on secure computational and communication tasks. Specifically, this work introduces a set of new QIA protocols that utilize controlled secure direct quantum communication. The proposed scheme facilitates mutual authentication between two users, Alice and Bob, with assistance from a third party, Charlie, using Bell states. A comprehensive security analysis demonstrates its robustness against impersonation, intercept-resend, and fraudulent authentication attacks. The comparative evaluation highlights its advantages over existing schemes. Additionally, this thesis presents two novel QKD protocols that eliminate the need for entanglement or ideal single-photon sources, making them feasible with commercially available photon sources. These protocols are rigorously proven to be secure against various attacks, including intercept-resend and certain collective attacks. Key rate bounds are established, demonstrating that specific classical pre-processing enhances the tolerable error threshold. PHD THESIS
We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.
This thesis deals with a detailed study of the unconditional security of Continuous-Variable (CV) Quantum Key Distribution (QKD). We consider general communication architectures based on both point-to-point and end-to-end principle. For the first case we develop an extensive analysis of the unconditional security of both one-way and two-way protocol under several eavesdropping conditions. We describe an effective post-processing strategy, to apply to one-way communications, that allows to neutralise general coherent attacks. This result motivates us to formulate the conjecture that the "de Finettization" of the classical data, typically adopted in the asymptotic limit of many signals exchanged in order to reduce the attacks from a general coherent to a collective one, may not be necessary for Gaussian one-way communication. For what it concerns two-way protocols we show that after the reduction of the general attack using the de Finetti symmetrization, two-mode coherent attacks are the optimal eavesdropping. Our cryptanalysis shows that the parties can exploit a strategy, in combination with the results obtained on the security of one-way protocols against two-mode coherent attacks. In fact we prove explicitly that two-way communication with Gaussian continuous variables is immune to general coherent attacks. This is possible exploiting the random opening and closing of the circuit by Alice (ON/OFF switching), in the limit of many uses of the channel. We then conclude that collective attacks represent, strictly, the best strategy available to Eve. We have then studied the general security of one-way protocol considering not just lossy channel, but extending the cryptanalysis to all physically allowed canonical forms attacks. Finally we extended the study of thermal CV-QKD to two-way communication at different frequencies, in the framework of optimal collective attacks. In the last part of this thesis we focused on CV-QKD considering a modern end-to-end configuration. We then extend CV quantum cryptography to a network configuration. We develop a detailed cryptoanalysis of a communication scheme based on an untrusted relay, assisting the parties during the preparation of the secret key. We find the optimal eavesdropping and prove, both theoretically and experimentally, the feasibility of high-rate CV-QKD over metropolitan distances with of-the-shelves devices.